What's so nice about the category of lenses?

Bryce Clarke – 17 February 2021

It has been 10 years since the category Lens, of categories and (delta) lenses, was introduced by Diskin, Xiong, and Czarnecki. Throughout this time, lenses have continued to be of interest to both computer scientists and category theorists alike, and much progress has been made in understanding their properties. However there are many aspects of the category Lens which remain unknown. For instance, understanding pullbacks in Lens has been important for developing a theory of symmetric lenses, yet very little is known about when they exist.

In this talk, I will discuss recent progress made towards understanding the category Lens, including the construction of certain classes of limits and colimits, monoidal structures, and factorisations systems. The talk is based on results originating from the Applied Category Theory 2020 Adjoint School, and is joint work with Michael Johnson, Emma Chollet, Maurine Songa, Vincent Wang, and Gioele Zardini.